To find the prime factorization of the given numbers in exponential form, we will break down each number into its prime factors step by step.
### (i) Prime Factorization of 72
1. Start dividing 72 by the smallest prime number, which is 2:
- 72 ÷ 2 = 36
2. Divide 36 by 2:
- 36 ÷ 2 = 18
3. Divide 18 by 2:
- 18 ÷ 2 = 9
4. Now, divide 9 by the next smallest prime number, which is 3:
- 9 ÷ 3 = 3
5. Finally, divide 3 by 3:
- 3 ÷ 3 = 1
Now, we can write the prime factors:
- 72 = 2 × 2 × 2 × 3 × 3
In exponential form:
- 72 = \(2^3 \times 3^2\)
### (ii) Prime Factorization of 360
1. Start dividing 360 by 2:
- 360 ÷ 2 = 180
2. Divide 180 by 2:
- 180 ÷ 2 = 90
3. Divide 90 by 2:
- 90 ÷ 2 = 45
4. Now, divide 45 by 3:
- 45 ÷ 3 = 15
5. Finally, divide 15 by 3:
- 15 ÷ 3 = 5
6. Now, 5 is a prime number.
Now, we can write the prime factors:
- 360 = 2 × 2 × 2 × 3 × 3 × 5
In exponential form:
- 360 = \(2^3 \times 3^2 \times 5^1\)
### (iii) Prime Factorization of 600
1. Start dividing 600 by 2:
- 600 ÷ 2 = 300
2. Divide 300 by 2:
- 300 ÷ 2 = 150
3. Divide 150 by 2:
- 150 ÷ 2 = 75
4. Now, divide 75 by 3:
- 75 ÷ 3 = 25
5. Finally, divide 25 by 5:
- 25 ÷ 5 = 5
6. Now, 5 is a prime number.
Now, we can write the prime factors:
- 600 = 2 × 2 × 2 × 3 × 5 × 5
In exponential form:
- 600 = \(2^3 \times 3^1 \times 5^2\)
### (iv) Prime Factorization of 2280
1. Start dividing 2280 by 2:
- 2280 ÷ 2 = 1140
2. Divide 1140 by 2:
- 1140 ÷ 2 = 570
3. Divide 570 by 2:
- 570 ÷ 2 = 285
4. Now, divide 285 by 3:
- 285 ÷ 3 = 95
5. Divide 95 by 5:
- 95 ÷ 5 = 19
6. Now, 19 is a prime number.
Now, we can write the prime factors:
- 2280 = 2 × 2 × 2 × 3 × 5 × 19
In exponential form:
- 2280 = \(2^3 \times 3^1 \times 5^1 \times 19^1\)
### (v) Prime Factorization of 4725
1. Start dividing 4725 by 3:
- 4725 ÷ 3 = 1575
2. Divide 1575 by 3:
- 1575 ÷ 3 = 525
3. Divide 525 by 3:
- 525 ÷ 3 = 175
4. Now, divide 175 by 5:
- 175 ÷ 5 = 35
5. Finally, divide 35 by 5:
- 35 ÷ 5 = 7
6. Now, 7 is a prime number.
Now, we can write the prime factors:
- 4725 = 3 × 3 × 3 × 5 × 5 × 7
In exponential form:
- 4725 = \(3^3 \times 5^2 \times 7^1\)
### Summary of Prime Factorizations:
1. \(72 = 2^3 \times 3^2\)
2. \(360 = 2^3 \times 3^2 \times 5^1\)
3. \(600 = 2^3 \times 3^1 \times 5^2\)
4. \(2280 = 2^3 \times 3^1 \times 5^1 \times 19^1\)
5. \(4725 = 3^3 \times 5^2 \times 7^1\)
